Fused Deposition Modelling (FDM) is an additive manufacturing-based rapid prototyping technology that has gained widespread attention due to its ability to produce complex geometries with relatively low cost and fast production time. However, the surface finish of the FDM printed parts can be adversely affected by the selection of input parameters, such as layer height, infill density, print temperature, etc. This study aims to investigate the impact of these parameters on surface roughness and optimize the FDM process to improve surface finish. Two optimization approaches were employed in the study to address this problem, namely the Response Surface Methodology (RSM) and the particle swarm optimization (PSO) method. The impacts of four factors, layer height, printing speed, infill density, and print temperature, on the surface roughness of Polylactic Acid (PLA) printed parts were evaluated. A Face-centred Central Composite Design (FCCD) was used to reduce the number of experiments and to optimize the process. Both RSM and PSO methods were employed to find the best combination of process parameters for minimum surface roughness. The results of the experiment indicated that the optimal settings for minimum surface roughness were a layer height of 0.10 mm, printing speed of 30.36 m/s, infill density of 77.10 %, and print temperature of 195.12 °C, resulting in a surface roughness value of 1.31 µm. From these findings, the PSO optimization method was found to be more effective than the RSM method, showing a significant improvement in surface roughness with a reduction of 13.5 %.